Implementation of combined footage stops in a computor organ

ABSTRACT

Combined footage stops are implemented in a computor organ of the type wherein musical notes are produced by computing successive sample point amplitudes of a musical waveshape and converting the amplitudes to sound as the computations are performed in real time. Each waveshape amplitude is obtained by evaluating those Fourier components comprising an incomplete set of harmonics for a first footage voice, and the fundamental and several low order odd harmonics of a voice of lower footage. In a preferred embodiment, an incomplete 8-foot harmonic series is employed, together with the first four odd harmonics of a 16-foot series. The 8-foot harmonics correspond in frequency to even harmonics of the 16-foot series. The missing 8-foot components are &#39;&#39;&#39;&#39;reinstated&#39;&#39;&#39;&#39; by the listener&#39;&#39;s ear. As a result, the combined voice is perceived just as though separate, complete spectra had been used to generate the waveshape. To implement shorter footage stops, certain of the 8-foot harmonics are excluded from the waveshape computation. For combined voices including shorter footage stops, the sum of the harmonic coefficients associated with the concurrently selected stops are used in the component calculations.

United Stat es Patent 11 1 OTHER PUBLICATIONS R. Scott, Linear Circuits, Addison-Wesley Publish- Deutsch May 7, 1974 IMPLEMENTATION OF COMBINED ing Company, Inc., copyright 1960, pp. 679-685.

FOOTAGE STOPS IN A COMPUTOR ORGAN Primary Examiner-Richard B. Wilkinson [75] Inventor; Ralph Deutsch Sherman Oaks, Assistant Examiner-Stanley J. Wttkowsk C lif Attorney, Agent, or F irm- Howard A. SllbCIZ Flam [73] Assignee: Nippon Gakki Seizo Kabushiki flimhfi 1 Kaisha, l-lamamatsu-shi, Japan 22 Filed: Jan. 31, 1973 [57-] ABSTRACT Combined footage stops are implemented in a compu- [21] 328302 tor organ of the type wherein musical notes are produced by computing successive sample point ampli- [52] US. Cl 84/ 1.01, .84/ 1.22, 84/ 1.23 tudes of a musical waveshape and converting the am- [51] Int. Cl. Glhy1/06, GlOh 5/02 'plitudes to sound as the computations are performed [58] Field of Search 84/1.0l, 1.03, 1.22, 1.23 in real time. Each waveshape amplitude is obtained by evaluating those Fourier components comprising an [56] References Cited incomplete set of harmonics for a first footage voice,

' UNITE-D STATES PATENTS and the fundamental and several low order odd har- 3 610 799 /1971 Watson 84/1.01 monies Ofa voice oflower footagea Preferred 3:639:91? 2/1972 Watson 84,101 X bodiment, an incomplete 8-foot harmonic series is em- 3,696,201 10/1972 Arsem et 1.34/10] ployed, together with the first four odd harmonics of a 3,697,661 10/1972 Deutsch 84/l.0l series Th -f h m nics rre pon in 3,740,450 6/1973 Deutsch.... 84/l.23 X frequency to even harmonics of the 16-foot series. 3,743,755 /1973 Wats The missing 8-foot components are reinstated" by 317553308 8973 Deutsch 84/1-O1 the listeners ear. As a result, the combined voice is 4 10/1973 fl X perceived just as though separate, complete spectra M42580 H1939 wmmms 84,123 x had been used to generate the waveshape. To imple- 3,000.252 9/1961 Wayne 84/l.0l 3515792 6/1970 Deutsch I I I 8403 ment shorter footage stops, certain of the 8-foot har- 3598892 vYamashim H 84mm momcs are excluded from the waveshape computa- 3,668,294 6/1972 Kameoka et 31" 34/101 tion. For combined voicesincluding shorter footage 3,723,633 3/1973 Adachi '84 1.01 p h m i h h rm nic coefficien s a ociated with the concurrently selected stops are used in the component calculations.

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BACKGROUND. OF THE INVENTION 1. Field of the Invention IThe present invention relates to implementation of combined footage stops in a computor organ.

2. Specific Related Applications The present invention is related to the inventors copending US. patent applications Ser. No. 225,883 filed Feb. 14, 1972 entitled COMPUTOR ORGAN, and Ser. No. 298,365 filed Oct. 17, 1972 entitled COMPUTOR ORGAN USING PARALLEL PROCESSING.

3. Description of the Prior Art In a pipe organ, when an 8-foot stop is actuated, notes are produced at the same pitch as the selected key. Thus if the manual key C is depressed, the note C (thekey ofC in octave 4) will be sounded. Should a 16-foot stop be selected, the organ will produce notes one octave lower than the corresponding key. Thus if the manual key C is depressed, C will be sounded. Notes of higher octaves are produced when foundation stops of other footage are selected. For example, a 4- foot stop and a 2-foot stop respectively result in-production of notes two and four octaves higher than the key being played.

Occasionally a musician will simultaneously select two or more stops of different footage. If a l6-foot and an 8-foot stop both are actuated, the organ simultaneously will produce sounds at both the notation frequency and one octave lower. An additional footage stop may be drawn to enhance certain harmonics ofthe used to enhance the fifth and 10th harmonics of a simultaneously selected 8-foot stop.

An objective of the present invention is the implementation of combined footage in a comp'utor organ of the type described in the above-mentioned patent applications. In such an instrument, musical sounds are generated by computing in real time the amplitudes at successive sample points of a musical waveshape and converting these amplitudes to sounds as the computations are carried out. Each amplitude is obtained by individually calculating the Fourier components contributing to that waveshape. A set of stored harmonic components specifies the relative amplitude of each such component; thus establishing the wave shape and hence the tonal quality of the produced sound.

Combined footage could be implemented in such acomputor organ by separately calculating, during each amplitude computation period, the harmonics associated with all selected stops. Should 8-foot and 1 6-foot stops simultaneously be selected, this seemingly straightforward approach would require calculation of twice the number of Fourier components normally calculated in the same time period, if only a single stop were selected. Since each sample point amplitude must be computed within a fixed time interval, such approach would require evaluation of individual components at twice the calculation speed required for a single footage stop. This is unsatisfactory, since the system speed requirements may exceed the capabilities of presently available integrated circuits. Alternatively, additional parallel computation channels could be used to evaluate the combined footage components. How'- ever, such added circuitry could as much as double the cost of the instrument.

The present invention provides a'novel implementation for combined footage which permits generation, e.g;, of simultaneously selected 8-foot and l6-foot stops without requiring either an increase in component calculation speed or the provision of additional computation channels.

SUMMARY OF THE INVENTION The foregoing objective is achieved by taking advantage of two factors. One is that the harmonics of an 8- foot series correspond to the even harmonics of a 16- foot stop. These corresponding harmonics need not be separately calculated when synthesizing a combined 8-foot and 16-foot tone. Secondly, certain harmonics can be eliminated without any appreciable loss in tonal quality of the synthesized organ sound. The present invention utilizes both factors. During each amplitude computation interval, the computor organ calculates the Fourier components of an incomplete 8-foot harmonic spectrum, and also calculates certain low order, odd harmonics of the-l6-foot spectrum. When combined to obtain the waveshape amplitude, the resultant sound has the tonal quality of combined 8- and l6-foot stops.

FIG. 1 illustrates typical 8-foot and l6-foot spectra generated by a computor organ using the inventive combined footage implementation. The 8-foot spectrav includes the harmonics 1 through 8, 10, 12, 14 and 16. The 9th, llth, 13th and 15th harmonics are not produced. These missing harmonics do not detract appreciably from the tonal quality of the generated organ sound. One reason is that for typical organ pipes, relatively little energy is contained in the higher harmonics. The first eight harmonics all are present; usually these are the strongest and dominate the tone coloring.

A more subtle reason relates to human sound perception. A psychoacoustic-effect occurs whereby the ear tends to rein sert the missing harmonics. Since the human auditory system is non-linear, an apparent interference or beat effect occurs between the harmonics which are present. For example, the 10th harmonic appears to beat with the fundamental to provide the apparent tone coloring of the missing 9th and llth harmonics. Similarly, the presence of the 12th, 14th and 16th harmonics causes the ear to reconstruct the missing llth, 13th and 15th harmonic components.

As noted earlier, the 8-foot harmonic components correspond to the even components of a l6.-foot series. In accordance with the present invention, the corresponding l6-foot even harmonic components (indicated by broken lines in FIG. 1) are not separately evaluated. However, the first four low order odd harmonics of the l6-foot series are calculated, as indicated by the solid lines in FIG. 1. These l6-foot components are evaluated during the time intervals normally allocated to calculation of those components which are missing from the 8-foot spectrum. The result is an effective 16- foot spectrum including the first eight harmonics, every other harmonic up to the 16th, and every fourth harmonic from the20th through the 32nd. The above described psychoacoustic effect causes the apparent reinsertion of the missing lo-foot harmonics in the perceived tone. With the present invention, excellent combined footage stops can be simulated even though only the sixteen separate components shown in solid lines in FIG. 1 are evaluated.

The timing. diagram of FIG. 2 illustrates how these 16 components may be evaluated within each fixedcomputation interval t, by a two-channel computor organ like that of FIG. 3. One computation channel 24A is allocated to calculation of the first eight 8-foot harmonics, as designated by the large numerals in the top row of FIG. 2. The remaining high order 8-foot harmonic components, and the four low order, odd harmonics of the 16-foot series are evaluated in a parallel computation channel 248. The small numerals in FIG. 2 designate the l6-foot components which correspond to the generated 8-foot components; these l6-foot components, indicated by the broken lines of FIG. 1, are not separately calculated by the computor organ.

The inventive combined footage implementation also permits generation of other foundation stops. As illustrated by FIG. 4, the 4-foot, 2-foot and l-foot foundation stops will have no missing components, even though the 8-foot series is incomplete. The 2 /a-foot and l 3/5-foot stops respectively will have two and one missing components. However, since these stops normally a-re selected to enhance specific harmonics in an 8-foot series, the missing components will have little practical effect on the perceived organ tones.

BRIEF DESCRIPTION OF THE DRAWINGS A detailed description of the invention will be made with reference to the accompanying drawings, wherein like numerals designate corresponding parts in the several figures. I

FIG. 1 shows the harmonic spectra of combined 8- foot and 16-foot stops as synthesized by a computor organ using the inventive combined footage implementation.

FIG. 2 is a timing diagram indicating the calculation intervals during which the spectral components of FIG. 1 are evaluated within each computor organ computation interval. Y

FIG. 3 is an electrical block diagram ofa computor organ employing the combined footage implementation of the present invention.

.FIGS. 4A through 4F show spectra of other'footage stops implemented with the present invention.

- FIG. 5 is an electrical block diagram showing a modification to the system of FIG. 3 for implementing the other footages of FIG. 4.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 1 The following detailed description is of the best presently contemplated modes of carrying out the invention. This description is not to be taken in a limiting sense, but is made merely for the purpose ofillustrating the general principles of the invention since the scope of the invention best is defined by the appended claims.

Structural and operational characteristics attributed to forms of the invention first described shall also be attributed to forms later described, unless such characteristics are obviously inapplicable or unless specific 22 and a sound system 23. The waveshape amplitude is computed for successive sample points at regular time intervals t Within each such interval t, the first eight harmonics of the 8-foot spectra (FIG. 1) are separately evaluated in a first processing channel 24A. Within each same interval 1, the first four odd harmonics of the 16400: spectra (FIG. 1 and the 10th, 12th,

14th and 16th 8-foot harmonic components are evaluated in a second parallel processing channel 248.

All of the components-are summed algebraically in an accumulator 25 which, at the end ofeachcomputation interval t contains the amplitude at the present sample point. This amplitude is provided to the digitalto-analog converter 22 via a gate 26 enabled by a 1: signal on a line 27. Computation of the amplitude for the next sample point immediately is initiated, so that the analog voltage supplied from the converter 17 comprises a musical waveshape generated in real time and having a spectral content characteristic of combined footage.

In the present invention, the amplitude contribution F1 of each 8-foot component is evaluated inaccor; dance with the following relationship:

F C sin ('rr/W) nqR for q =l,2,3

where R is a frequency number associated with the note selected at the keyboard switches 12. The number n designates the harmonic component being evaluated. Thus for the implementation of FIG. 1,

n=l,2,3,4,5,6,7,8,l0,12,14,16 corresponding respectively to the harmonics shown in solid lines in FIG. 1.

8 are evaluated in the channel 24A; the values F for n=l0,l2,l4,l6' are evaluated inthe channel 24B.

The amplit u de contribution fm 'l of each l 6 foot odd harmonic component is evaluated in accordance with the following equation:

wherein n=l ,3, 5,7-and wherein C is a harmonic coefficient specifying the relative amplitude of the respective n'th 16-foot harmonic component. These values F also are evaluated in the processing, channel 248.

The waveshape amplitude x,,(qR) for each sample point qR is given by the relationship:

It is this value x (qR) which is obtained in the accumulator 25 during each computation interval 2, and which which the harmonic components are calculated; Such 5 system timing is established by a clock 29 which provides pulses at intervals I to a counter 30 of modulo W/2 8. The counter 30 produces consecutive output signals t through t on the correspondinglydesignated lines. The signals, slightly delayed in a delay unit 31, serve as the computation interval pulses I; on the line 27. For various gating functions described below, the timing signals through t are combined by an OR-gate 32 and provided to a line 33. The pulses tops,

through r all are supplied via an OR-gate 34 to a line 35. All eight timing signals 1 through I appear on a line 36 supplied by an OR-gate 37.

In the computor organ 20, a set of frequency numbers R corresponding to the notes of the instrument is stored in a frequency number memory 39. A note inter- 2O val adder 40 contains the value qR identifying the sample point at which the waveshape amplitude presently is being evaluated. This value qR is incremented at the beginning of each computation interval by adding the selected frequency number R to the previous contents of the adder 40. To this end, the value R is gated to the adder 40 via a gate 41 enabled by the t signal on the line 27. Preferably the adder 40 is of modulo W/2.

To calculate the first eight 8-foot harmonic components, the values nqR for n= 1,2,3, 8 areobtained in a harmonic interval adder 42 which is cleared by the t, signal at the end of each amplitude computation cy,- cle. Upon occurrence of the first clock pulse r of each computation cycle, the present value qR contained in the note interval adder is entered into 35 the harmonic interval adder 42 via a line 43 and a gate 44 enabled by the pulses on the line 36. At each subsequent clock pulse 1, through t the value qR is added to the previous contents of the adder 42. As a result, the harmonic interval adder 42 will contain the 4 An address decoder 45a accesses from a sinusoid 45 table 46a the value sin (1r/ W) nqR corresponding to the argument nqR received via a line 47 from the harmonic interval adder 42. The sinusoid table 46a may comprise a read-only memory storing values of sin (rr/W) 0 for 0 s 0 2W at intervals of D, where D is called the resolution constant of the memory.

The value sin (rr/W) nqR, supplied via a line 48a, is multiplied by the coefficient C for the corresponding n harmonic by a multiplier 49a. The multiplication product represents the amplitude F,," of the n" low order 8-foot harmonic component, and is supplied via a line 50a, an adder 51 and a line 52 to the accumulator 25. The appropriate coefficient C, is accessed from a harmonic coefficient memory 53a, described in more detail below, under the direction of a memory address control 54a also receiving the signals I,.,,, through via the line 36. The coefficient C,, is supplied to the multiplier 49a via a line 55a.

' As indicated by the diagram of FlG. 2, the firstfour low order 16-foot odd harmonics are calculated in the channel 248 during the respective timing intervals r through 1 These calculations are carried out in accordance with equation 2 above; To this end, the values nq(R/2) for n"= l,3,5,7 are established in a harmonic interval adder 56 during the respective timing intervals t through t Y i The component F is evaluated during the first interval r The value nq(R/2) q( R/2) is obtained in the adder 56 by gating the signal qR from the line 43 to a divide-by-two divider circuit 57 via a gate 58 enabled by the r signal. The output of the divider 57, corresponding to the value q(R/2) is entered into the harmonic interval adder 56 via the line 59'. .An address decoder 45b accesses from a' sinusoid table 46b the value sin (1r/W)[q(,R/2)] corresponding to'the argument q( R/2) received'from the harmonic interval adder 56 via an OR gate 61. The accessed sin value, supplied 'viaa line 48b, is multiplied by the coef-' ficientc =C 'for the corresponding first odd 16-foot harmonic by a multiplier 49b. The coefficient C is obtained via a line 55b from a harmonic coefficient memory 53b accessed by a memory address control 54b also receiving the timing signals tc101 through t via the line 36. The multiplication product, representing the amplitude F is supplied via a line 50b to the adder 51. The adder 51 adds the'component F to the component F which is concurrently evaluated in the channel 24A. The sum lator 25.

The next three 16-foot odd harmonics (n=3,5,7) are calculated during the computation intervals 1 through r Ateach such interval, the valueqR from the line 43 is added to the contents of the harmonic interval addgSQvia agate 62 enabled by the pulses r through t on the line 33. Thusfaf timefijffie 7 56 will contain the value n'q( R/2) 3q(R/2) (R/2) qR. Similarly, at intervals r and t the contents of the adder 56 will be 5q(R/2) (R/2) 2qR and 7q(R/2) (R/2) 3qR respectively. Conveniently, duringthe same intervals t,.,,- through I' the values qR, '2qR and 3qR- already are present on the line 43 from the adder 40.

The address decoder 45b and sinusoid table 46b operate as before to supply the designated sin values via the lines 48b to the multiplier 49 for multiplication by the corresponding harmonic coefficients C 440 C and c respectively. The multiplication products provided to the line 50b at the times r t and r respectively represent the values F for n=3,5,7.

1 These values are summed with the concurrently evaluthrough t To this end, a gate 65 enabled by the timing signals on the line 35 supplies the value nqR from the line 47 to a multiply-by-two multiplier circuit 66. The output 2nqR from the multiplier 66 is provided via a line 67 and the OR-gate 61 to the address decoder Recall that at time r the contents of the harmonic. interval adder 42 is nqR 5qR. Accordingly, at the interval t the argument ZnqR l OqR will 'be provided is supplied via the line 52 to the accumuadder table 46b. This is exactly the argument lOqR) necessary to calculate the th 8-foot harmonic component. The sinusoid table 45b, the multiplier 49b and the harmonic coefficient memory 53b operate as above described to provide the value F via the line 50b to the adder 51.

Similarly, at the time intervals 1 through t the values 6qR, 7qR and 8qR are present on the line 47. Accordingly, the arguments supplied to the decoder 45b will be l2qR, l4qR, and l6qR respectively. Accordingly, the components for n=1 2, l4, 16 will be calculated in the processing channel 24B.

In this manner the computor organ calculates exactly those components shown as solid lines in FIG. 1. The generated waveshape, the sample point amplitude of which are obtained in the accumulator 25, has a harmonic spectra characteristic of combined-footage. The resultant sounds produced by the computor organ 20 of FIG. 3 have the tonal quality of simultaneously selected 8-foot and 16-foot stops.

The specific voicing of the produced sounds will depend on the stored values of the harmonic coefficients C and C,,. This of course is a design choice, however the following Table l lists appropriate values of C and C,,' which will simulate a diapason voice. The values C through C are stored in the memory 53a; the remain ing coefficients listed in Table l are stored in the memory 53b.

The frequency numbers R stored in the memory 39 are related to the fundamental frequencies of the musical notes produced by the computor organ 20, to the computation time interval t and to the number of amplitude sample points N for the note of highest fundamental frequency f produced by the organ. For example, if the frequency number R for such note of highest frequency is selected as unity, then with a computation time interval t, given by t; =8t l/Nf exactly N sample point amplitudes-will be computed for that note. The values R for notes of lower frequency readily can I be ascertained, knowing that the frequency ratio of any two' contiguous notes in an equally tempered musical scale is"\/[ In general, the frequency numbers R for notes other than that of highest frequency f will be non-integers.

By way of example, the following Table II lists the frequency and frequency number R for each notein octave six. The note C (the key of C in octave 7) is designated as the note of highest fundamental frequency produced by the computor organ 20, and hence is assigned the frequency number R of unity. In this example, N=2W=32 sample points are computed for the note C this value of N being satisfactory for accurate synthesis for an organ pipe or most other musical Using the modification of FIG. 5, the computor organ 20 (FIG. 3) can produce other footage stops such as those having the spectra of FIGS. 4A.through 4F. Separate memories store the harmonic coefficients for each stop; in each memory the coefficient value zero is stored for all harmonic absent in the spectra of the associated stop. A switchingarrangement permits selction by the musician of any one or more footage stops.

bined by appropriate OR gates 71, 72a, 72b and adders 73a, 73b, 74a, 74b, 75a, 75b and supplied to the multipliers 49a, 49b via the respective lines 55aand 55b. This arrangement permits selection of any individual footage stop, or any combination of such stops.

If the stop switch ST alone is'closed, the computor organ 20 will generate an 8-foot voice having the incomplete harmonic spectra shown in solid lines in FIGS. 1 and 4A. To this end, the memory 81a contains coefficient values C through C inclusive. These values are supplied to the multiplier 49a via the adder 73a, the

second input of which remains at zero since no stop tab other than ST, is selected. The memory 81b contains the harmonic coefficients C C 2, C1 and C stored in locations accessed during the successive time intervals t,.,, through r The memory 81b stores the value zero in those locations accessed at times r through r Thus during the intervals r through 1 the value zero is supplied from the memory 81b via the OR-gate 71 and the adder 73b to the multiplier 49b. Accordingly, the channel 248 makes no contribution to the computed waveshape during those time intervals when, were a 16-foot stop also selected, the first four low order, 16-foot odd harmonics would be computed. During the intervals I through t the coefficients C C C and C respectively are supplied to the multiplier 49b, so that the corresponding th, 12th, 14th and 16th 8-foot harmonics are evaluated..The resultant waveshape of the harmonic spectra of FIGS. 1 and 4A, characteristic of an 8-foot voice. A

To generate a combined 8-foot and l6-foot voice using the modification of FIG. 5, the stops ST and ST both are closed. The memories 81a, 81b provide the coefficients describedabove, resulting in production of the incomplete 8-foot spectra of FIG. 1. A memory 82b stores the harmonic coefficient values C C C and C in locations accessed during the successive intervals 2 through 1 These values are supplied via the OR- gate 71 and the adder 73b to the multiplier 49b. Accordingly, when both the ST,, and ST stop tabs are selected, the memories 81a, 81b and 82b together function exactly like the memories 53a, 53b of FIGS, and the combined 8-foot and l6-foot spectra of F1G.'l is generated.

A 16-foot spectra alone can be generated by closing only the switch ST Again, the memory 82b provides the coefficients appropriate to generate the first four 16-foot odd harmonics. The first eight l6-foot even harmonics are generated with coefficients provided by the memory 81a. The resultant l6-foot spectra will correspond to that shown in the lower portion of FIG. 1, except that there will be no harmonic higher than the 16th (n'=l6). A 4-foot voice is produced when the switch 5T is closed. The memories 83a, 83b contain the values C,, for all even values of n between n=2 and n=l6. As indicated in Table III below, these values are stored in locations accessed during the calculation intervals used for production of the corresponding components of the 8-foot spectra of FIG. 4A. All other positions of the memories 83a, 83b store zeros. When the 4-foot stop ST, is selected, the computor organ 20 will produce a sound having the harmonic spectra of FIG.

Similarly, a 2'-foot, l-foot, 2%-foot or I 3/5-foot voice is produced when the corresponding switch 8T ST,, 8T or ST is closed. Table III also lists the contents of the harmonic coefficient memories 84a through 87b used with these footage stopsjThe coefficient values given in Table III are illustrative of a diapason voice; other values may be used to provide different voicing. However, those stored zero valued coefficients should remain zero to insure generation of spectra like those of FIGS. 4C through 4F.

- When the 2 %-foot stop is selected, only those components shown in solid lines in FIG. 4E are generated. The third and fifth harn onics, c orrespor dingin frequency to the eighth (n=8) and 16th (n 16) harmonics of the 8-foot spectra, are not produced. Similarly, when respond to components which are absent in the incomplete 8-foot spectra (FIG. 4A) generated by the computor organ 20.

TABLE III Harmonic Stored Typical Co- Interval During Coeffi- Harmonic efficient Which Storage Footage cient Coeffi- Value Location is Memory cient* (Diapason) Accessed 4-foot 830 C 127 1 C, 71 1,, C,, 90 1 C 36 1 83b C 23 1,,

12 I 28 rm u 8 n? m 8 run 2-foot 840 C, 127 I C11 71 m 84b c,. 90 m mm l-foot 85 a C 127 I,.,,,, 85b C,., 7| 1 2 biz-foot 860 c, 127 1 C 71 r 86!) C 36 r,,,,, 1 3/5-foot 870 C 127 r,,,

87b c 71 r,,,,

* All other stored harmonic coefficient values are zero.

' As noted earlier, the shorter footage stops often are used to enhance certain harmonics of another stop. This is illustrated by the spectra of FIGS. 4A and 4F for the case when an 8-foot and l 3/5-foot stop simultaneously are selected. In this instance, the fifth and 10th 8-foot harmonics are emphasized. These harmonics have the resultant amplitudes shown by broken lines 90, 91 in FIG. 4A, and specified by the sums of the harmonic coefficients of both selected stops.

For the combined 8-and l 3/5-foot stop, at the time t separate non-zero harmonic coefficients are accessed from both the memories 81a and 87a. The latter coefficient is supplied via the OR-gate 72a and the adders 75a, 74a to the adder 73a wherein it is summed with the coefficient accessed from the. memory 810. The sum is supplied via the line 55a to the multiplier 49a, so that the calculated fifth (n=5) harmonic component has the resultant amplitude shown by the line 90 in FIG. 4A.

Similarly, in channel 248 at time non-zero coefficient values are accessed from both the memories 81b and 87b. The latter is supplied via the OR-gate 72b and the adders 75b, 74b to the adder 73b where it is summed with the coefficient accessed from the memory 81b. The sum is supplied via the line 55b to the multiplier 49b. Thus the evaluated 10th 8-foot harmonic has the enhanced amplitude shown by the broken line 91 in FIG. 4A. At all times other than r zero-valued coefficients are accessed from the 'l 3/5-foot memories 87a, 87b so that the other harmonics of the 8-foot series are not enhanced.

The computor organ 20 of FIG. 3 readily may be implemented using conventional microelectronic. integrated circuits ICs). .Thus the, frequency number memory 39 may comprise an IC read-only memory programmed to contain the frequency numbers R listed in Table 11 above. A useful 1C read-only memory is the Signetics type 8223 which is user programmable and includes addressing circuitry. Such an IC also may be used as the harmonic coefficient memory 53a, 53b 70a or 70b, with the self-contained addressing circuitry serving as the associated memory address decoder 54a, 54b, 540, or 54b. Typical stored harmonic coefficient values are listed in Tables I and III.

1 1 The adders 40, 42 and 56 may be implemented using conventional IC adders; such circuits include the Signetics 8260 arithmetic logic element, the Sign etics 8268 gated full adder, and the Texas Instruments SN 5483 and SN 7483 4-bit binary full adders. In FIG. 3, the adjectives note interval and harmonic interval are used to indicate the function of the adder in the computor organ 20. Thus the contents qR of the adder 25 designates the sample point interval at which the note amplitude presently is being evaluated. Similarly, the adders 42 and 56 contain the values nqR specifying the sample point intervals of the 8-foot harmonics being evaluated in the respective channels 24A and 248.

The accumulator 25 may comprise IC adders connected as shown e.g., in the standard text by Ivan Flores entitled Computor Logic, Prentice-Hall, 1960. Each sinusoid table 46a, 46b and its address decoder 459,

45b may comprise an IC read-only memory containing sinusoid values with appropriate resolution D. Memories preprogrammed with sinusoid values are available commercially, as typified by the Texas Instruments TMS 4405 integrated circuit. The multipliers 49a, 49b are conventional, the adjective harmonic amplitude indicating that the circuit multiplies the sin value (from the line 48a or 48b) by the appropriate harmonic coefficient (from the line 55a or 55b) to obtain as a product the amplitude of the harmonic component then being calculated in the channel 24A, 248 containing the multiplier. Likewise, the remaining components of the computor organ 20 (FIG. 3) are conventional.

Intending to claim all novel, useful and unobvious features shown or described, the applicant makes the following claims: I

1. In an electronic musical instrument of the type wherein the amplitudes of a waveshape are computed at regular time intervals 2, from stored harmonic coefficients, musical notes being produced from said computed amplitudes as said computations are carried out, the improvement comprising:

first means for calculating an incomplete set of harmonics ofa first footage voice from said storedcoefficients during certain calculation subintervals within each regular interval t second means for calculating, during other calculation subintervals within each such interval t harmonics associated with a voice of footage different from said first footage, and third means for obtaining eachwaveshape amplitude by combining all components calculated during each time interval 1,.

2. A musical instrument according to claim 1 wherein said first footage voice is an 8-foot stop, wherein said different footage voice is a l6-foot stop, and wherein said second means includes a memory storing a set of harmonic coefficients for said 16-foot stop, said set including non-zero coefficients only for odd l 6-foot harmonics, calculation of both said 8-foot incomplete set sical notes having the tonal quality ofa stop of footage shorter than said first footage.

.12 4. A musical instrument accordingto claim 3 including;

- a first memory means, connected to provide to said first means a set of harmonic coefficients associated with said first footage. voice and a second memory means connected to provide to said first means a selected separate set of harmonic coefficients associated with another voice of shorter footage, the spectra of said shorter footage voice including only some harmonics of said first footage, said set of shorter footage coefficients including non,-zero valued coefficients only for said some harmonics, allother coefficients being zero valued,

. so that during each regular time interval 1,, when coefficients for at least one other shorter footage voice for use in the harmonic component calculations, said other shorter footage voice thereby enhancing the amplitude of certain components in said first set.

6. A musical instrument according to claim 1 and having parallel processing channels, certain harmonic 7 components of said incomplete set being calculated in one of said channels during the same subintervals that certain of saidlonger footage odd harmonics are calculated in another of said channels. I

7. A musical instrument providing combined footage, comprising: I

parallel processing channels for calculating within a regular'time interval t, first and second subsets of Fourier components associated with the amplitude of a musical waveshape at a certain sample point, said first subset including harmonic components of a first footage which correspond to even harmonics of a second footage of lower. fundamental frequency, said second subset including odd harmonic components of said second footage, said first and second footages respectively being 8-foot and 16- foot', each 8-foot component F being calculated according to the equation F C sin '(rr/W) nqR wherein C is a coefficient associated with the n" 8-foot harmonic, wherein R is a frequency number associated with each note selected for production by said instrument, wherein q=l,2,3 so that qR designates said certain sample point and wherein Wis the total number of components evaluated to obtain each amplitude, each l6-foot component being calculated according to the equation F C,, sin r/W) n'q(R/2) wherein C,, is a coefficient associated with the n" l6-foot harmonic component,

note selection means for'providing a value R associated with a selected note, means for providing to said first channel the values nqR for certain values of n within each regular time interval t, means forproviding to said second channel values nqR for certain non-consecutive values of n and values n'q(R/2) for certain odd valuesof n, accumulator means for combining the Fourier com- 'ponents calculated .by said processing channels during each time interval t, to obtain the waveshape amplitude at said certain sample point, control means for causing said processing channels and said accumulator means to perform said calculating and combining operations repetitively for successive sample points during successive time intervals t and converter means for producing musical sounds from said obtained amplitudes as said calculating and combining are carried out in real time, said sounds having a tonal quality characteristic of combined footage,

and wherein each processing channel comprises:

a memory storing harmonic coefficients associated with components calculated in that channel,

means for obtaining the values sin ('n/W) nqR and sin (1r/ W) nq( R/2) corresponding to the value of the argument nqR and nq( R/2) respectively provided to that channel, and

a multiplier for multiplying the appropriate harmonic coefficient from said memory means by said obtained sin value and providing the product to said accumulator means.

8. A musical instrument according to claim 7 wherein for said first channel said certain values of n are n=1,2, 7,8, and wherein for said second channel said certain non-consecutive values of n are n=l0,l2,l4,l6 and wherein said certain odd values of n are n'=l ,3,5,7.

-9. A musical instrument according to claim 7 wherein all stored values of C,, are zero so that no 16-foot odd harmonics are generated, and further comprising means for implementing stops of other footage comprising:

separate memory means storing harmonic coefficients associated respectively with said other footage stops, and I stop selection means for accessing from said separate memory means coefficients associated with selected other footage stops and for providing said accessed coefficients to said multipliers.

10. A musical instrument according to claim 6 wherein said other footage associated coefficients are used instead of said 8-foot coefficients C said instrument then producing an other than S-foot voice.

11. A musical instrument according to claim 9 wherein said other footage associated coefficients are used in addition to said 8-foot coefficients, said instruments then producing an 8-foot voice having certain enhanced harmonics. Y

12. An instrument according to claim 7 wherein instead of a combined 8-foot and l6-foot voice, a combined voice consisting of an 8-foot stop and another shorter footage stop is produced, comprising:

a. means for disconnecting from one processing channel the harmonic coefficient memory containing the l6-foot harmonic coefficients,

b. a storage device for storing a set of harmonic coefficients for another voice of shorter footage, said set including non-zero valued coefficients only for components corresponding to certain harmonics of said first subset, all other coefficients being zerovalued, and

. switching means for connecting to said parallel processing channels said storage device and the memory containing said first subset of 8-foot harmonic coefficients, so that during each regular time interval t those 8-foot harmonic components also included in the spectra of said shorter footage voice are enhanced. 

1. In an electronic musical instrument of the type wherein the amplitudes of a waveshape are computed at regular time intervals tx from stored harmonic coefficients, musical notes being produced from said computed amplitudes as said computations are carried out, the improvement comprising: first means for calculating an incomplete set of harmonics of a first footage voice from said stored coefficients during certain calculation subintervals within each regular interval tx, second means for calculating, during other calculation subintervals within each such interval tx, harmonics associated with a voice of footage different from said first footage, and third means for obtaining each waveshape amplitude by combining all components calculated during each time interval tx.
 2. A musical instrument according to claim 1 wherein said first footage voice is an 8-foot stop, wherein said different footage voice is a 16-foot stop, and wherein said second means includes a memory storing a set of harmonic coefficients for said 16-foot stop, said set including non-zero coefficients only for odd 16-foot harmonics, calculation of both said 8-foot incomplete set of harmonics and said odd 16-foot harmonics resulting in musical notes having a combined 8-foot and 16-foot tonal quality.
 3. A musical instrument according to claim 2 wherein no longer footage odd harmonics are calculated, and including means for calculating less than all harmonics of said incomplete set of first footage, the resultant musical notes having the tonal quality of a stop of footage shorter than said first footage.
 4. A musical instrument according to claim 3 including; a first memory means, connected to provide to said first means a set of harmonic coefficients associated with said first footage voice and a second memory means connected to provide to said first means a selected separate set of harmonic coefficients associated with another voice of shorter footage, the spectra of said shorter footage voice including only some harmonics of said first footage, said set of shorter footage coefficients including non-zero valued coefficients only for said some harmonics, all other coefficients being zero valued, so that during each regular time interval tx, when said selected separate set of coefficients is provided to said first means, only those first footage components also included in the spectra of said selected shorter footage voice are calculated.
 5. A musical instrument according to claim 4 further comprising means for combining the stored harmonic coefficients for said first set and the stored harmonic coefficients for at least one other shorter footage voice for use in the harmonic component calculations, said other shorter footage voice thereby enhancing the amplitude of certain components in said first set.
 6. A musical instrument according to claim 1 and having parallel processing channels, certain harmonic components of said incomplete set being calculated in one of said channels during the same subintervals that certain of said longer footage odd harmonics are calculated in another of said channels.
 7. A musical instrument providing combined footage, comprising: parallel processing channels for calculating within a regular time interval tx first and second subsets of Fourier components associated with the amplitude of a musical waveshape at a certain sample point, said first subset including harmonic components of a first footage which correspond to even harmonics of a second footage of lower fundamental frequency, said second subset including odd harmonic components of said second footage, said first and second footages respeCtively being 8-foot and 16-foot, each 8-foot component F8(n) being calculated according to the equation F8(n) Cn sin ( pi /W) nqR wherein Cn is a coefficient associated with the nth 8-foot harmonic, wherein R is a frequency number associated with each note selected for production by said instrument, wherein q 1,2,3 . . . so that qR designates said certain sample point and wherein W is the total number of components evaluated to obtain each amplitude, each 16-foot component being calculated according to the equation F16(n) Cn'' sin ( pi /W) n''q(R/2) wherein Cn'' is a coefficient associated with the nth 16-foot harmonic component, note selection means for providing a value R associated with a selected note, means for providing to said first channel the values nqR for certain values of n within each regular time interval tx means for providing to said second channel values nqR for certain non-consecutive values of n and values n''q(R/2) for certain odd values of n'', accumulator means for combining the Fourier components calculated by said processing channels during each time interval tx to obtain the waveshape amplitude at said certain sample point, control means for causing said processing channels and said accumulator means to perform said calculating and combining operations repetitively for successive sample points during successive time intervals tx, and converter means for producing musical sounds from said obtained amplitudes as said calculating and combining are carried out in real time, said sounds having a tonal quality characteristic of combined footage, and wherein each processing channel comprises: a memory storing harmonic coefficients associated with components calculated in that channel, means for obtaining the values sin ( pi /W) nqR and sin ( pi /W) n''q(R/2) corresponding to the value of the argument nqR and n''q(R/2) respectively provided to that channel, and a multiplier for multiplying the appropriate harmonic coefficient from said memory means by said obtained sin value and providing the product to said accumulator means.
 8. A musical instrument according to claim 7 wherein for said first channel said certain values of n are n 1,2, . . . 7,8, and wherein for said second channel said certain non-consecutive values of n are n 10,12,14,16 and wherein said certain odd values of n'' are n'' 1,3,5,7.
 9. A musical instrument according to claim 7 wherein all stored values of Cn'' are zero so that no 16-foot odd harmonics are generated, and further comprising means for implementing stops of other footage comprising: separate memory means storing harmonic coefficients associated respectively with said other footage stops, and stop selection means for accessing from said separate memory means coefficients associated with selected other footage stops and for providing said accessed coefficients to said multipliers.
 10. A musical instrument according to claim 6 wherein said other footage associated coefficients are used instead of said 8-foot coefficients Cn, said instrument then producing an other than 8-foot voice.
 11. A musical instrument according to claim 9 wherein said other footage associated coefficients are used in addition to said 8-foot coefficients, said instruments then producing an 8-foot voice having certain enhanced harmonics.
 12. An instrument according to claim 7 wherein instead of a combined 8-foot and 16-foot voice, a combined voice consisting of an 8-foOt stop and another shorter footage stop is produced, comprising: a. means for disconnecting from one processing channel the harmonic coefficient memory containing the 16-foot harmonic coefficients, b. a storage device for storing a set of harmonic coefficients for another voice of shorter footage, said set including non-zero valued coefficients only for components corresponding to certain harmonics of said first subset, all other coefficients being zero-valued, and c. switching means for connecting to said parallel processing channels said storage device and the memory containing said first subset of 8-foot harmonic coefficients, so that during each regular time interval tx those 8-foot harmonic components also included in the spectra of said shorter footage voice are enhanced. 